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equidigital n.  and  self-describing n.

First numbers that belong to both sets:

10123133, 10153133, 10153331, 10173133, 10173331, 10183133, 10183331, 10193331, 10213223, 10233221, 10311533, 10311733, 10311833, 10313315, 10313317, 10313319, 10322123, 10322321, 10331531, 10331631, 10331831, 10331931, 10333117, 10333119, 12103331, 12153331, 12163133, 12163331, 12173133, 12183133, 12183331, 12193133, 12193331, 12311033, 12311433, 12311633, 12311733, 12311833, 12311933, 12313317, 12313318, 12313319, 12331031, 12331531, 12333115, 12333118, 12333119, 14153331, 14173331, 14183133, 14193331, 14311533, 14311633, 14311833, 14311933, 14313315, 14313319, 14331031, 14331631, 14331731, 14331831, 14333115, 15103133, 15103331, 15123133, 15143331, 15163331, 15173133, 15183133, 15183331, 15193133, 15213223, 15233221, 15311033, 15311233, 15311433, 15311633, 15311833, 15322123, 15331031, 15331231, 15331431, 15331631, 15331931, 15333117, 15333118, 15333119, 16123331, 16143331, 16153133, 16153331, 16173133, 16173331, 16183133, 16233221, 16311433, 16311533, 16311733, 16311833, 16313315, 16313317, 16322321, 16331231, 16331531, 16331831, 16333115, 16333117, 16333118, 17103133, 17103331, 17123133, 17143133, 17143331, 17311033, 17311233, 17311533, 17311633, 17311933, 17331031, 17331231, 17333119, 18103133, 18103331, 18123133, 18123331, 18143331, 18153133, 18163331, 18193133, 18213223, 18233221, 18311233, 18311433, 18311633, 18311933, 18313315, 18313319, 18322123, 18331031, 18331231, 18331431, 18331531, 18331931, 18333115, 19123133, 19123331, 19143133, 19143331, 19153133, 19153331, 19183133, 19213223, 19311233, 19311833, 19313312, 19313315, 19331031, 19331231, 19331731, 19331831, 19333115.